We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of the standard Extremal Types Theorem. Typical studies in distributional robustness involve computing worst case estimates over a model uncertainty region expressed in terms of the Kullback-Leibler discrepancy. We go beyond standard distributional robustness in that we investigate different forms of discrepancies, and prove rigorous results which are helpful for understanding the role of a putative model uncertainty region in the context of extreme quantile estimation. Finally, we illustrate our data-driven method in various settings, including examples showing how standard EVT can significantly underestimate quantiles of interest.

中文翻译：

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关于分布稳健的极值分析

我们在极值理论（EVT）的背景下研究分布稳健性。我们提供了一种数据驱动的方法，以一种针对标准极端类型定理应用基础的错误模型假设具有鲁棒性的方式估算极端分位数。分布鲁棒性的典型研究涉及在以Kullback-Leibler差异表示的模型不确定性区域上计算最坏情况的估计。我们超越了标准的分布稳健性，因为我们研究了不同形式的差异，并证明了严格的结果，这些结果有助于理解假定的模型不确定性区域在极端分位数估计的情况下的作用。最后，我们说明了各种设置下的数据驱动方法，